We know, courtesy of FiveThirtyEight, that foreign policy got the most questions at Tuesday’s Democratic Party debate. This matches what went down at the first GOP presidential debate in August. So it would seem that foreign policy will be a pret-ty, pret-ty good topic for discussion for the rest of the campaign.

Except that one of the things I learned at my conference last week on foreign policy on the campaign hustings is that foreign policy doesn’t matter that much at all to voters. Indeed, UCLA’s Lynn Vavreck took a shiv to the “foreign policy could be pivotal in 2016” meme, and the results were as gruesome as you could imagine. According to Vavreck, it’s still the economy, stupid. The pollsters and public opinion specialists in attendance pretty much confirmed Vavreck’s conclusion.

On the one hand, this isn’t news to me. On the other hand, it does raise a question: If voters aren’t too exercised about foreign policy, then what role, if any, does it play in the campaign? Thanks to a very diverse group of participants — campaign advisers, journalists, scholars, Democrats, Republicans, even a donor — I learned a lot (like, keep Carly Fiorina as far away from the reins of power as possible). See, for example, conference participant Rosa Brooks for her lessons learned. Here are my top five take-home messages:

1) Foreign policy knowledge is a necessary but not sufficient condition for electoral success. Political scientists like Vavreck can make confident statements about general election dynamics. Nomination fights are a different matter, and serious candidates have suffered from foreign policy stumbles, miscues and past errors at that stage of the campaign (see: Rick Perry in 2012, Hillary Clinton in 2008, Howard Dean in 2004). Hoover Institution fellow Kori Schake suggested — and many other participants seconded — the notion that foreign policy is a “gateway issue” for voters. As Rosa Brooks put it Wednesday:

Voters need to be convinced that a candidate has enough knowledge, strength, and wisdom to handle foreign-policy matters, but once a candidate establishes minimal foreign-policy credibility, voters are content to leave the details to the experts. Establishing foreign-policy credentials isn’t sufficient to get anyone into the White House, but maybe it’s a necessary precondition.

But this leads to …

2) Campaigns treat foreign policy issues as unexploded landmines. Listening to past and current campaign operatives, it was striking how much they talked about national security and foreign policy questions with extreme wariness. To them, the global situation is so fluid that they fear any comment on a current situation could come back to haunt them later in the campaign. Comparatively speaking, the campaign people thought of economic issues as much more stable.

To be clear, it’s not that campaigns will avoid foreign policy talk — they know it’s necessary. They just also believe that there are serious risks in talking about it. Which leads t o…

3)  There is a trade-off between specific and vague campaign promises on foreign policy. In a perfect world, campaigns want to issue broad foreign policy visions during a campaign. Speeches and policy statements that offer overarching visions help to demonstrate a candidate’s worldview without locking in any commitments.

The problem is that voters, experts and the media pay more attention to specific foreign policy promises than to broad generalities. And candidates are human beings. So sometimes they make specific promises to appease key constituencies and generate media interest. An additional political virtue of such promises is that, if the candidate wins, there’s a mandate to execute those pledges. The problem is that those pledges can be extremely difficult to carry out. One ex-Romney adviser discussed the serious challenges of his “label China a currency manipulator on day one” pledge.

Not surprisingly, some victorious candidates have to reverse course after getting elected. But that leads to …

4) Campaigns take foreign policy promises seriously. Precisely because politicians take credibility and reputation seriously, they really, really do not like to go back on their word when it comes to campaign promises. This does not mean it won’t happen, but it was surprising to me how vehement both campaign operatives and scholars were on this point. If at all possible, winning presidential candidates will carry out their promises. It usually fails to happen only when the candidate, after winning, learns about the second- and third-order effects of implementing those promises. So silly, empty pledges like renegotiating NAFTA appear to be the exception and not the rule.

And finally …

5) Knowledgeable foreign policy advisers cannot compensate for an uninformed candidate. A common refrain from foreign policy neophytes is that they will bring in smart foreign policy people when they get elected (see Donald Trump, Ben Carson, Fiorina, etc.). George Washington University’s Elizabeth Saunders is doing some fascinating research, however, that suggests there are hard limits on this approach. In essence, the problem is that novice foreign policy leaders are less able to detect groupthink from their advisers, or process conflicting advice from them. And lest one think this isn’t an issue, compare how the exact same group of advisers performed for George H.W. Bush and George W. Bush.

So if you care about foreign policy and haven’t picked a candidate yet, ask yourself the following question: Which politician do you trust refereeing among squabbling foreign policy advisers?